Where are the high symmetry points on a graphene band structure?

In summary, the location of high-symmetry points in DFT simulations depends on the choice of unit cell and can be different for larger real-space unit cells. The points in reciprocal space correspond to the periodicity of extended states in real space. To calculate the band structure, you can either use software tools like xcrysden or manually compare reciprocal lattice vectors to a Brillouin zone diagram. It is recommended to solve a Hückel model for graphene first to gain a better understanding.
  • #1
gwr
1
0
Hi!

Is anyone familiar with generating band structures from DFT simulations? I am using graphene, and am trying to plot the electronic structure at the high symmetry points (K, M, and gamma). Grappling to understand this theory, my questions are:

1. Is the location of the high symmetry points dependent upon the choice of the reciprocal lattice vectors, or only the geometry of the first Brillouin zone? For example, in my DFT simulation, I am using a supercell, so not the primitive cell. Hence my lattice vectors and thus reciprocal vectors are not primitive. Does this affect the whereabouts of the high symmetry points in my case?

2. Do any of the high symmetry points, as defined in reciprocal space, coincide with any physical features of the crystal lattice in real space? For example, I initially thought that the K and K' points coincided with the C-atom sites, but now think that this is incorrect.

3. In light of the above, is there a particularly easy way to calculate what lines I should plot the band structure along in order to map out the gamma-M-K-gamma path?

Any assistance would be greatly appreciated!

Thanks,
gwr
 
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  • #2
if u r doing dft in quantum espresso, then just open input scf file with xcrysden, then go to tool and then select the k path selection. u can select any path u desire. then choose number of k points. use them in input scf file for band replacing k points by the .pwscf file u obtained from xcrysden. then u can calculate bands.x for band structure.
 
  • #3
1. The location of high-symmetry points very much depends on the choice of the unit cell. A larger real-space unit cell (like a supercell) will have a different Brillouin zone, and therefore different high-symmetry points. In certain reduced units (i.e. in units of the real-space unit cell lattice vector), the expressions for the high-symmetry points may look the same.

2. The points in reciprocal space don't so much correspond to points in real space, but rather to the wavelength or periodicity of extended states in real space.

3. The method suggested by saroj, using xcrysden, is one simple way. Alternatively, you can just look at the documentation (e.g. for quantum espresso), which gives the implied reciprocal lattice vectors. Then you can compare to a diagram of the Brillouin zone for your unit cell, to figure out where your high-symmetry points are (just a little bit of geometry :smile:).
 
  • #4
I would recommend you to try to solve a Hückel model for graphene first by hand before using quantum chemical software. This reduces to solving a 2x2 matrix eigenvalue problem and you can sketch the eigenfunctions for the high symmetry points to get a feeling for what all is about.
 

1. What is Graphene band structure?

Graphene band structure refers to the arrangement of energy levels or bands in graphene, a unique two-dimensional material made of a single layer of carbon atoms arranged in a hexagonal lattice. In graphene, the energy levels of electrons are described by a band structure that consists of two bands, the valence band and the conduction band, which are separated by a bandgap.

2. How does the band structure of graphene differ from other materials?

The band structure of graphene is different from other materials because of its unique atomic arrangement and two-dimensional nature. Unlike most materials, graphene has a linear energy dispersion relation, meaning that the energy of electrons is directly proportional to their momentum. This gives graphene its exceptional mechanical, electrical, and thermal properties.

3. What is the significance of the band structure in graphene?

The band structure of graphene is significant because it determines the material's electronic properties. Due to the linear energy dispersion relation, graphene has high electron mobility, making it an excellent conductor of electricity. The band structure also plays a crucial role in determining the material's optical, thermal, and mechanical properties.

4. How is the band structure of graphene measured?

The band structure of graphene can be measured using various techniques such as angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and Raman spectroscopy. These techniques involve shining light or electrons on the graphene sample and measuring the energy and momentum of the emitted particles, which can then be used to determine the band structure.

5. Can the band structure of graphene be modified?

Yes, the band structure of graphene can be modified by applying external forces, such as an electric or magnetic field, or by introducing defects or impurities into the material. These modifications can alter the energy levels and bandgap of graphene, leading to changes in its electronic, optical, and mechanical properties. This ability to manipulate the band structure makes graphene a promising material for a wide range of applications in electronics, energy, and healthcare.

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